trihemitone

The semitones are of two different sizes, because the trihemitone is composed of a tone and a limma; the tone in turn is composed of a limma and an apotome; thus the trihemitone equals 2 limmata and 1 apotome.

The trihemitone may also be found as a perfect 4th minus a tone.

In prime factor notation this interval is written 253-3; thus, its 2,3-monzo is [5 -3, > .

The trihemitone can be calculated thus by regular fractional math:

4 9 4 8 32
- ÷ - = - * - = --
3 8 3 9 27

or by vector addition:

2 3
[ 2 -1] 4/3
- [-3 2] ÷ 9/8
--------- = -------
[ 5 -3] 32/27

Below is a diagram illustrating these descriptions, on an approximate logarithmic scale: